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instead of the usual $\partial \sigma = 2b$. See this presentation.

instead of the usual $\partial \sigma = 2b$. See this presentation.

instead of the usual $\partial \sigma = 2b$.

instead of the usual $\partial \sigma = 2b$. See this presentation.

It would be interesting to compare these higher homotopy groupoid structures, and the weak structures in common current parlance, with the vision of the algebraic topologists of the early 20th for higher dimensional versions of the nonabelian fundamental group. Since the finding in 1932 that Cech's definition of higher homotopy groups, which he submitted to the ICM at Zurich, led to abelian groups, this has seemed to be a mirage.

It would be interesting to compare these higher homotopy groupoid structures, and the weak structures in common current parlance, with the vision of the algebraic topologists of the early 20th century for higher dimensional versions of the nonabelian fundamental group. Since the finding in 1932 that Cech's definition of higher homotopy groups, which he submitted to the ICM at Zurich, led to abelian groups, this has seemed to be a mirage.